# RS Aggarwal Solutions for Class 7 Maths Chapter 6 Algebraic Expressions

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Exercise 6A

Exercise 6B

Exercise 6C

Exercise 6D

## Exercise 6A

(i) 5x, 7x, -6x

Solution:-

In the above questions terms having the same literal factors are like terms.

= 5x + 7x + (-6x) â€¦ [âˆµ + Ã— – = -]

Add terms having same sign first,

= 5x + 7x â€“ 6x

= 12x â€“ 6x

= 6x

(ii) (3/5)x, (2/3)x, (-4/5)x

Solution:-

In the above questions terms having the same literal factors are like terms.

= (3/5)x + (2/3)x + (-4/5)x

LCM of 5, 3, and 5 is 15

= (9x + 10x â€“ 12x)/ 15

= (19x â€“ 12x)/ 15

= (7/15)x

(iii) 5a2b, -8a2b, 7a2b

Solution:-

In the above questions terms having the same literal factors are like terms.

= 5a2b – 8a2b + 7a2b

= 12 a2b – 8a2b

= 4a2b

(iv) (3/4)x2, 5 x2, -3x2, -(1/4) x2

Solution:-

In the above questions terms having the same literal factors are like terms.

= (3/4)x2 + 5x2 – 3x2 – (1/4) x2

= (3/4)x2– (1/4) x2 + 5x2 – 3x2

= ((3-1)/4)x2 + 2x2

= (2/4)x2 + 2x2

= (1/2)x2 + 2x2

= ((1 + 4)/2)x2

= (5/2)x2

(v) x â€“ 3y + 4z, y â€“ 2x â€“ 8z, 5x â€“ 2y â€“ 3z

Solution:-

Required sum,

= (x â€“ 3y + 4z) + (y â€“ 2x â€“ 8z) + (5x â€“ 2y â€“ 3z)

Collecting like terms,

= x â€“ 2x + 5x â€“ 3y + y â€“ 2y + 4z â€“ 8z â€“ 3z

= (1 â€“ 2 + 5)x + (- 3 + 1 â€“ 2)y + (4 â€“ 8 â€“ 3)z

= 4x â€“ 4y â€“ 7z

(vi) 2x2 â€“ 3y2, 5x2 + 6y2, -3x2 â€“ 4y2

Solution:-

Required sum,

= (2x2 â€“ 3y2) + (5x2 + 6y2) + (-3x2 â€“ 4y2)

Collecting like terms,

= 2x2 + 5x2 â€“ 3x2 â€“ 3y2 + 6y2 â€“ 4y2

= (2 + 5 â€“ 3)x2 + (â€“ 3 + 6 â€“ 4)y2

= 4x2 â€“ y2

(vii) 5x â€“ 2x2 â€“ 8, 8x2 â€“ 7x â€“ 9, 3 + 7x2 â€“ 2x

Solution:-

Required sum,

= (5x â€“ 2x2 â€“ 8) + (8x2 â€“ 7x â€“ 9) + (3 + 7x2 â€“ 2x)

Collecting like terms,

= 2x2 + 8x2 + 7x2 + 5x â€“ 7x â€“ 2x â€“ 8 â€“ 9 + 3

= (-2 + 8 + 7)x2 + (5 â€“ 7 â€“ 2)x + ( â€“ 8 â€“ 9 + 3)

= 13x2 â€“ 4x â€“ 14

(viii) (2/3)a â€“ (4/5)v + (3/5)c, -(3/4)a â€“ (5/2)b + (2/3)c, (5/2)a + (7/4)b â€“ (5/6)c

Solution:-

Required sum,

= [(2/3)a â€“ (4/5)b + (3/5)c] + [-(3/4)a â€“ (5/2)b + (2/3)c] + [(5/2)a + (7/4)b â€“ (5/6)c]

Collecting like terms,

= (2/3)a -(3/4)a + (5/2)a â€“ (4/5)b â€“ (5/2)b + (7/4)b + (3/5)c + (2/3)c â€“ (5/6)c

= [(2/3) – (3/4) + (5/2)]a + [(-4/5) â€“ (5/2) + (7/4)]b + [(3/5) + (2/3) â€“ (5/6)]c

= [(8 – 9 + 30)/12)a] + [(-16 -15 +30)/20)b] + [(18 + 20 â€“ 25)/ 30)c]

= (29/12)a +- (31/20)b + (13/30)c

(ix) (8/5)x + (11/7)y + (9/4)xy, (-3/2)x â€“ (5/3)y â€“ (9/5)xy

Solution:-

Required sum,

[(8/5)x + (11/7)y + (9/4)xy] + [(-3/2)x â€“ (5/3)y â€“ (9/5)xy]

Collecting like terms,

= [(8/5)x – (3/2)x] + [(11/7)y â€“ (5/3)y] + [(9/4)xy â€“ (9/5)xy]

= (1/10)x â€“ (2/21)y + (9/20)xy

(x) (3/2)x3 – (1/4)x2 + (5/3), (-5/4)x3 + (3/5)x2 â€“ x + (1/5), -x2 + (3/8)x â€“ (8/15)

Solution:-

Required sum,

= (3/2)x3 – (1/4)x2 + (5/3), (-5/4)x3 + (3/5)x2 â€“ x + (1/5), -x2 + (3/8)x â€“ (8/15)

Collecting like terms,

= [(3/2)x3 – (5/4)x3] + [- (1/4)x2 + (3/5)x2 -x2] + [â€“ x + (3/8)x] + [(5/3) + (1/5) â€“ (8/15)]

= (1/4)x3 â€“ (13/20)x2 â€“ (5/8)x + (4/3)

2. Subtract :

(i) -8xy from 7xy

Solution:-

The difference of two like terms is a like term whose coefficient is the difference of the numerical coefficient of the two like terms.

Then,

= (7 â€“ (-8))xy

= 15xy

(ii) X2 from -3x2

Solution:-

The difference of two like terms is a like term whose coefficient is the difference of the numerical coefficient of the two like terms.

Then,

= (-3 â€“ 1)x2

= -4x2

(iii) (x â€“ y) from (4y â€“ 5x)

Solution:-

The difference of two like terms is a like term whose coefficient is the difference of the numerical coefficient of the two like terms.

We have,

= (4y â€“ 5x) â€“ (x â€“ y)

Change the sign of each term of the expression to be subtracted and then add.

= 4y â€“ 5x â€“ x + y

= (-5x â€“ x) + (4y – y)

= -5x + 3y)

= 3y â€“ 5x

(iv) (a2 + b2 â€“ 2ab) from (a2 + b2 + 2ab)

Solution:-

The difference of two like terms is a like term whose coefficient is the difference of the numerical coefficient of the two like terms.

We have,

= (a2 + b2 + 2ab) – (a2 + b2 â€“ 2ab)

Change the sign of each term of the expression to be subtracted and then add.

= a2 + b2 + 2ab â€“ a2 â€“ b2 + 2ab

= (1 -1)a2 + (1 â€“ 1)b2 + (2 + 2)ab

= (0)a2 + (0)b2 + (4)ab

= 4ab

(v) (x2 â€“ y2) from (2x2 â€“ 3y2 + 6xy)

Solution:-

The difference of two like terms is a like term whose coefficient is the difference of the numerical coefficient of the two like terms.

We have,

= (2x2 â€“ 3y2 + 6xy) – (x2 â€“ y2)

Change the sign of each term of the expression to be subtracted and then add.

= 2x2 â€“ 3y2 + 6xy â€“ x2 + y2

= (2x2 – x2) + (â€“ 3y2 + y2) + 6xy

= (2 â€“ 1)x2 + (â€“ 3 + 1)y2 + 6xy

= 1x2 + (â€“ 2y2) + 6xy

= 1x2 â€“ 2y2 + 6xy

(vi) (x â€“ y + 3z) from (2z â€“ x – 3y)

Solution:-

The difference of two like terms is a like term whose coefficient is the difference of the numerical coefficient of the two like terms.

We have,

= (2z â€“ x – 3y) – (x â€“ y + 3z)

Change the sign of each term of the expression to be subtracted and then add.

= 2z â€“ x – 3y â€“ x + y â€“ 3z

= (2z â€“ 3z) + (â€“ x â€“ x) + (- 3y + y)

= (2 â€“ 3)z + (â€“ 1 â€“ 1)x + (- 3 +1)y

= -1z â€“ 2x – 2y

3. Subtract (2a â€“ 3b + 4c) from the sum of (a + 3b â€“ 4c), (4a â€“ b + 9c) and (-2b + 3c â€“ a)

Solution:-

First we find the sum of (a + 3b â€“ 4c), (4a â€“ b + 9c) and (-2b + 3c â€“ a)

= (a + 3b â€“ 4c) + (4a â€“ b + 9c) + (-2b + 3c â€“ a)

= (a + 3b â€“ 4c + 4a â€“ b + 9c – 2b + 3c â€“ a)

= (a + 4a â€“ a) + (3b â€“ b â€“ 2b) + (-4c + 9c + 3c)

= (1 + 4 â€“ 1)a + (3 â€“ 1 â€“ 2)b + (-4 + 9 + 3)c

= 4a + (0)b + 8c

=4a + 8c

Then,

Subtract (2a â€“ 3b + 4c) from (4a + 8c)

= (4a + 8c) – (2a â€“ 3b + 4c)

= 4a + 8c â€“ 2a + 3b â€“ 4c

= (4a â€“ 2a) + (3b) + (8c â€“ 4c)

= 2a + 3b + 4c

## Exercise 6B

Find the products:

1. 3a2 Ã— 8a4

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= (3 Ã— 8) Ã— (a2 Ã— a4)

= (24) Ã— (a2+4) â€¦ [âˆµ am Ã— an = am+n]

= (24) Ã— (a6)

= 24 a6+

2. -6x3 Ã— 5x2

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= (-6 Ã— 5) Ã— (x3 Ã— x2)

= (-30) Ã— (x3+2) â€¦ [âˆµ am Ã— an = am+n]

= (-30) Ã— (x5)

= -30 a5

3.(-4ab) Ã— (-3a2bc)

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= (-4 Ã— -3) Ã— (a Ã— a2) Ã— (b Ã— b) Ã— c

= (12) Ã— (a1+2) Ã— (b1+1) Ã— c â€¦ [âˆµ am Ã— an = am+n]

= (12) Ã— (a3) Ã— (b2) Ã— c

= 12a3b2c

4. (2a2b3) Ã— (-3a3b)

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= (2 Ã— -3) Ã— (a2 Ã— a3) Ã— (b3 Ã— b)

= (-6) Ã— (a2+3) Ã— (b3+1) â€¦ [âˆµ am Ã— an = am+n]

= (-6) Ã— (a5) Ã— (b4)

= -6a5b4

5. (2/3)x2y Ã— (3/5)xy2

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= [(2/3) Ã— (3/5)] Ã— (x2 Ã— x) Ã— (y Ã— y2)

= [(2Ã—3)/ (3Ã—5)] Ã— (x2+1) Ã— (y1+2) â€¦ [âˆµ am Ã— an = am+n]

= [(2Ã—1)/ (1Ã—5)] Ã— (x3) Ã— (y3)

= [2/5]x3y3

6. (-3/4)ab3 Ã— (-2/3)a2b4

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= [(-3/4) Ã— (-2/3)] Ã— (a Ã— a2) Ã— (b3 Ã— b4)

= [(-3Ã—-2)/ (4Ã—3)] Ã— (a1+2) Ã— (b3+4) â€¦ [âˆµ am Ã— an = am+n]

= [(-1Ã—-1)/ (2Ã—1)] Ã— (a3) Ã— (b7)

= [1/2]a3b7

7. (-1/27)a2b2 Ã— (-9/2)a3bc2

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= [(-1/27) Ã— (-9/2)] Ã— (a2 Ã— a3) Ã— (b2 Ã— b) Ã— c2

= [(-1Ã—-9)/ (27Ã—2)] Ã— (a2+3) Ã— (b2+1) Ã— c2 â€¦ [âˆµ am Ã— an = am+n]

= [(-1Ã—-1)/ (3Ã—2)] Ã— (a5) Ã— (b3) Ã— c2

= [1/6]a5b3c2

8. (-13/5)ab2c Ã— (7/3)a2bc2

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= [(-13/5) Ã— (7/3)] Ã— (a Ã— a2) Ã— (b2 Ã— b) Ã— (c Ã— c2)

= [(-13Ã—7)/ (5Ã—3)] Ã— (a1+2) Ã— (b2+1) Ã— (c1+2) â€¦ [âˆµ am Ã— an = am+n]

= [-91/ 15] Ã— (a3) Ã— (b3) Ã— c3

= [-91/15]a3b3c3

9. (-18/5)x2z Ã— (-25/6)xz2y

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= [(-18/5) Ã— (-25/6)] Ã— (x2 Ã— x) Ã— (z Ã— z2) Ã— (y)

= [(-18Ã—-25)/ (5Ã—6)] Ã— (x2+1) Ã— (z1+2) Ã— (y) â€¦ [âˆµ am Ã— an = am+n]

= [(-3Ã—-5)/ (1Ã—1)] Ã— (x3) Ã— (z3) Ã— y

= 15x3z3y

10. (-3/14)xy4 Ã— (7/6)x3y

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= [(-3/14) Ã— (7/6)] Ã— (x Ã— x3) Ã— (y4 Ã— y)

= [(-3Ã—7)/ (14Ã—6)] Ã— (x1+3) Ã— (y4+1) â€¦ [âˆµ am Ã— an = am+n]

= [(-1Ã—1)/ (2Ã—2)] Ã— (x4) Ã— (y5)

= (-1/4)x4y5

11. (-7/5)x2y Ã— (3/2)xy2 Ã— (-6/5)x3y3

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= [(-7/5) Ã— (3/2) Ã— (-6/5)] Ã— (x2 Ã— x Ã— x3) Ã— (y Ã— y2 Ã— y3)

= [(-7Ã—3Ã—-6)/ (5Ã—2Ã—5)] Ã— (x2+1+3) Ã— (y1+2+3) â€¦ [âˆµ am Ã— an = am+n]

= [(-7Ã—3Ã—-2)/ (5Ã—1Ã—5)] Ã— (x6) Ã— (y6)

= (63/25)x6y6

12. 2a2b Ã— (-5)ab2c Ã— (-6)bc2

Solution:-

The coefficient of the product of two monomials is equal to the product of their coefficients.

The variable part in the product of two monomials is equal to the product of the variables in the given monomials.

Then,

= [(2) Ã— (-5) Ã— (-6)] Ã— (a2 Ã— a) Ã— (b Ã— b2 Ã— b) Ã— (c Ã— c2)

= [60] Ã— (a2+1) Ã— (b1+2+1) Ã— (c1+2) â€¦ [âˆµ am Ã— an = am+n]

= [60] Ã— (a3) Ã— (b4) Ã— (c3)

= [60]a3b4c3

## Exercise 6C

Find each of the following products:

1. 4a(3a + 7b)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over addition, we have:

P Ã— (q + r) = (p Ã— q) + (p Ã— r)

Now,

= (4a Ã— 3a) + (4a Ã— 7b)

= (12a2 + 28ab) â€¦ [âˆµ am Ã— an = am+n]

2. 5a(6a – 3b)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over subtraction, we have:

P Ã— (q – r) = (p Ã— q) – (p Ã— r)

Now,

= (5a Ã— 6a) – (5a Ã— 3b)

= (30a2 – 15ab) â€¦ [âˆµ am Ã— an = am+n]

3. 8a2(2a + 5b)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over addition, we have:

P Ã— (q + r) = (p Ã— q) + (p Ã— r)

Now,

= (8a2 Ã— 2a) + (8a2 Ã— 5b)

= (16a3 + 40a2b) â€¦ [âˆµ am Ã— an = am+n]

4. 9x2(5x + 7)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over addition, we have:

P Ã— (q + r) = (p Ã— q) + (p Ã— r)

Now,

= (9x2 Ã— 5x) + (9x2 Ã— 7)

= (45x3 + 63x2) â€¦ [âˆµ am Ã— an = am+n]

5. ab(a2 â€“ b2)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over subtraction, we have:

P Ã— (q – r) = (p Ã— q) – (p Ã— r)

Now,

= (ab Ã— a2) – (ab Ã— b2)

= (a3b + ab3) â€¦ [âˆµ am Ã— an = am+n]

6. 2x2(3x â€“ 4x2)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over subtraction, we have:

P Ã— (q – r) = (p Ã— q) – (p Ã— r)

Now,

= (2x2 Ã— 3x) – (2x2 Ã— 4x2)

= (6x3 â€“ 8x4) â€¦ [âˆµ am Ã— an = am+n]

7.(3/5)m2n(m + 5n)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over addition, we have:

P Ã— (q + r) = (p Ã— q) + (p Ã— r)

Now,

= ((3/5)m2n Ã— m) + ((3/5)m2n Ã— 5n)

= ((3/5)m3n + 3m2n2) â€¦ [âˆµ am Ã— an = am+n]

8. -17x2(3x â€“ 4)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over subtraction, we have:

P Ã— (q – r) = (p Ã— q) – (p Ã— r)

Now,

= (-17x2 Ã— 3x) – (-17x2 Ã— 4)

= (-51x3 + 68x2) â€¦ [âˆµ am Ã— an = am+n]

9. (7/2)x2((4/7)x + 2)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over addition, we have:

P Ã— (q + r) = (p Ã— q) + (p Ã— r)

Now,

= ((7/2)x2 Ã— (4/7)x) + ((7/2)x2 Ã— 2)

= ((7Ã—4)/ (2Ã—7))x3 + ((7Ã—2)/(2Ã—1))x2 â€¦ [âˆµ am Ã— an = am+n]

= ((1Ã—2)/ (1Ã—1))x3 + ((7Ã—1)/(1Ã—1))x2

= (2)x3 + (7)x2

10. -4x2y(3x2 â€“ 5y)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over subtraction, we have:

P Ã— (q – r) = (p Ã— q) – (p Ã— r)

Now,

= (-4x2y Ã— 3x2) – (-4x2y Ã— -5y)

= (-12x4y + 20x2y2) â€¦ [âˆµ am Ã— an = am+n]

11. (-4/27)xyz((9/2)x2yz â€“ (3/4)xyz2)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over subtraction, we have:

P Ã— (q – r) = (p Ã— q) – (p Ã— r)

Now,

= ((-4/27)xyz Ã— (9/2)x2yz) – ((-4/27)xyz Ã— (-3/4)xyz2)

= ((-4Ã—9)/ (27Ã—2))x3y2z2 + ((-4Ã—-3)/(27Ã—4))x2y2z3 â€¦ [âˆµ am Ã— an = am+n]

= ((-2Ã—1)/ (3Ã—1))x3y2z2 + ((-1Ã—-1)/(9Ã—1))x2y2z3

= (-2/3)x3y2z2 + (1/9)x2y2z3

12. 9t2(t + 7t3)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over addition, we have:

P Ã— (q + r) = (p Ã— q) + (p Ã— r)

Now,

= (9t2 Ã— t) + (9t2 Ã— 7t3)

= (9t3 + 63t5) â€¦ [âˆµ am Ã— an = am+n]

13. 10a2(0.1a â€“ 0.5b)

Solution:-

Let p, q and r be three monomials.

Then, by distributive law of multiplication over subtraction, we have:

P Ã— (q – r) = (p Ã— q) – (p Ã— r)

Now,

= (10a2 Ã— 0.1a) – (10a2 Ã— 0.5b)

= (1a3 â€“ 5a2b) â€¦ [âˆµ am Ã— an = am+n]

## Exercise 6D

Find each of the following products:

1. (5x + 7) (3x + 4)

Solution:-

Suppose (a + b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a + b) Ã— (c + d) = a Ã— (c + d) + b Ã— (c + d) = (a Ã— c + a Ã— d) + (b Ã— c + b Ã— d)

= ac + ad + bc + bd

Let,

a= 5x, b= 7, c= 3x, d= 4

Now,

= 5x Ã— (3x + 4) +7 Ã— (3x + 4)

= [(5x Ã— 3x) + (5x Ã— 4)] + [(7 Ã— 3x) + (7 Ã— 4)]

= [15x2 + 20x + 21x + 28]

= [15x2 + 41x + 28]

2. (4x – 3) (2x + 5)

Solution:-

Suppose (a – b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) Ã— (c + d) = a Ã— (c + d) – b Ã— (c + d) = (a Ã— c + a Ã— d) – (b Ã— c + b Ã— d)

= ac + ad – bc – bd

Let,

a= 4x, b= 3, c= 2x, d= 5

Now,

= 4x Ã— (2x + 5) -3 Ã— (2x + 5)

= [(4x Ã— 2x) + (4x Ã— 5)] – [(3 Ã— 2x) + (3 Ã— 5)]

= [8x2 + 20x – 6x – 15]

= [8x2 + 14x – 15]

3. (x – 6) (4x + 9)

Solution:-

Suppose (a – b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) Ã— (c + d) = a Ã— (c + d) – b Ã— (c + d) = (a Ã— c + a Ã— d) – (b Ã— c + b Ã— d)

= ac + ad – bc – bd

Let,

a= x, b= 6, c= 24x, d= 9

Now,

= x Ã— (4x + 9) -6 Ã— (4x + 5)

= [(x Ã— 4x) + (x Ã— 9)] – [(6 Ã— 4x) + (6 Ã— 9)]

= [4x2 + 9x – 24x – 54]

= [4x2 – 15x – 54]

4. (5y – 1) (3y – 8)

Solution:-

Suppose (a – b) and (c – d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) Ã— (c – d) = a Ã— (c – d) – b Ã— (c – d) = (a Ã— c – a Ã— d) – (b Ã— c – b Ã— d)

= ac – ad – bc + bd

Let,

a= 5y, b= 1, c= 3y, d= 8

Now,

= 5y Ã— (3y – 8) -1 Ã— (3y – 8)

= [(5y Ã— 3y) + (5y Ã— -8)] – [(1 Ã— 3y) + (1 Ã— -8)]

= [15y2 â€“ 40y â€“ 3y + 8]

= [15y2 â€“ 43y + 8]

5. (7x + 2y) (x + 4y)

Solution:-

Suppose (a + b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a + b) Ã— (c + d) = a Ã— (c + d) + b Ã— (c + d) = (a Ã— c + a Ã— d) + (b Ã— c + b Ã— d)

= ac + ad + bc + bd

Let,

a= 7x, b= 2y, c= x, d= 4y

Now,

= 7x Ã— (x + 4y) +2y Ã— (x + 4y)

= [(7x Ã— x) + (7x Ã— 4y)] + [(2y Ã— x) + (2y Ã— 4y)]

= [7x2 + 28xy + 2yx + 8y2]

= [7x2 + 30xy + 8y2]

6. (9x + 5y) (4x + 3y)

Solution:-

Suppose (a + b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a + b) Ã— (c + d) = a Ã— (c + d) + b Ã— (c + d) = (a Ã— c + a Ã— d) + (b Ã— c + b Ã— d)

= ac + ad + bc + bd

Let,

a= 9x, b= 5y, c= 4x, d= 3y

Now,

= 9x Ã— (4x + 3y) +5y Ã— (4x + 3y)

= [(9x Ã— 4x) + (9x Ã— 3y)] + [(5y Ã— 4x) + (5y Ã— 3y)]

= [36x2 + 27xy + 20yx + 15y2]

= [36x2 + 47xy + 15y2]

7. (3m â€“ 4n) (2m â€“ 3n)

Solution:-

Suppose (a – b) and (c – d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) Ã— (c – d) = a Ã— (c – d) – b Ã— (c – d) = (a Ã— c – a Ã— d) – (b Ã— c – b Ã— d)

= ac – ad – bc + bd

Let,

a= 3m, b= 4n, c= 2m, d= 3n

Now,

= 3m Ã— (2m â€“ 3n) -4n Ã— (2m â€“ 3n)

= [(3m Ã— 2m) + (3m Ã— -3n)] – [(4n Ã— 2m) + (4n Ã— -3n)]

= [6m2 â€“ 9mn â€“ 8mn + 12n2]

= [6m2 â€“ 17mn + 12n2]

8. (0.8x â€“ 0.5y) (1.5x â€“ 3y)

Solution:-

Suppose (a – b) and (c – d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) Ã— (c – d) = a Ã— (c – d) – b Ã— (c – d) = (a Ã— c – a Ã— d) – (b Ã— c – b Ã— d)

= ac – ad – bc + bd

Let,

a= 0.8x, b= 0.5y, c= 1.5x, d= 3y

Now,

= 0.8x Ã— (1.5x â€“ 3y) – 0.5y Ã— (1.5x â€“ 3y)

= [(0.8x Ã— 1.5x) + (0.8x Ã— -3y)] – [(0.5y Ã— 1.5x) + (0.5y Ã— -3y)]

= [1.2x2 â€“ 2.4xy â€“ 0.75yx + 1.5y2]

= [1.2x2 â€“ 3.15xy + 1.5y2]

9. ((1/5)x + 2y) ((2/3)x â€“ y)

Solution:-

Suppose (a + b) and (c – d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a + b) Ã— (c – d) = a Ã— (c – d) + b Ã— (c – d) = (a Ã— c – a Ã— d) + (b Ã— c – b Ã— d)

= ac – ad + bc – bd

Let,

a= (1/5)x, b= 2y, c= (2/3)x, d= y

Now,

= (1/5)x Ã— ((2/3)x â€“ y) + 2y Ã— ((2/3)x â€“ y)

= [((1/5)x Ã— (2/3)x) + ((1/5)x Ã— -y)] + [(2y Ã— (2/3)x) + (2y Ã— -y)]

= [(2/15)x2 – (1/5)xy + (4/3)yx – 2y2)]

= [(2/15)x2 + (17/15) xy – 2y2]

10. ((2/5)x â€“ (1/2)y) (10x â€“ 8y)

Solution:-

Suppose (a – b) and (c – d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) Ã— (c – d) = a Ã— (c – d) – b Ã— (c – d) = (a Ã— c – a Ã— d) – (b Ã— c – b Ã— d)

= ac – ad – bc + bd

Let,

a= (2/5)x, b=(1/2)y, c= 10x, d= 8y

Now,

= (2/5)x Ã— (10x â€“ 8y) – (1/2)y Ã— (10x â€“ 8y)

= [((2/5)x Ã— 10x) + ((2/5)x Ã— -8y)] – [((1/2)y Ã— 10x) + ((1/2)y Ã— -8y)]

= [4x2 â€“ (16/5)xy â€“ 5yx + 4y2]

= [4x2 â€“ (41/5)xy + 4y2]

11. ((3/4)a + (2/3)b) (4a + 3b)

Solution:-

Suppose (a – b) and (c – d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a + b) Ã— (c + d) = a Ã— (c + d) + b Ã— (c + d) = (a Ã— c + a Ã— d) + (b Ã— c + b Ã— d)

= ac + ad + bc + bd

Let,

a= (3/4)a, b=(2/3)b, c= 4a, d= 3b

Now,

= (3/4)a Ã— (4a + 3b) + (2/3)b Ã— (4a + 3b)

= [((3/4)a Ã— 4a) + ((3/4)a + 3b)] – [((2/3)b Ã— 4a) + ((2/3)b Ã— + 3b)]

= [3a2 + (9/4)ab + (8/3)ab + 2b2]

= [3a2 + ((27+32)/12)ab + 2b2]

= [3a2 + (59/12)ab + 2b2]

12. (x2 â€“ a2) (x â€“ a)

Solution:-

Suppose (a – b) and (c – d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) Ã— (c – d) = a Ã— (c – d) – b Ã— (c – d) = (a Ã— c – a Ã— d) – (b Ã— c – b Ã— d)

= ac – ad – bc + bd

Let,

a= x2, b= a2, c= x, d= a

Now,

= x2 Ã— (x â€“ a) – a2 Ã— (x â€“ a)

= [(x2 Ã— x) + (x2 Ã— -a)] – [(a2 Ã— x) + (a2 Ã— -a)]

= [x3 â€“ x2a â€“ a2x + a3]

13. (3p2 + q2) (2p2 â€“ 3q2)

Solution:-

Suppose (a + b) and (c – d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a + b) Ã— (c – d) = a Ã— (c – d) + b Ã— (c – d) = (a Ã— c – a Ã— d) + (b Ã— c – b Ã— d)

= ac – ad + bc – bd

Let,

a= 3p2, b= q2, c= 2p2, d= 3q2

Now,

= 3p2Ã— (2p2 â€“ 3q2) + q2 Ã— (2p2 â€“ 3q2)

= [(3p2Ã— 2p2) + (3p2Ã— -3q2)] + [(q2 Ã— 2p2) + (q2 Ã— -3q2)]

= [6p4 â€“ 9p2q2 + 2q2p2 â€“ 3q4)]

= [6p4 â€“ 7p2q2 â€“ 3q4]

14. (2x2 â€“ 5y2) (x2 + 3y2)

Solution:-

Suppose (a – b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) Ã— (c + d) = a Ã— (c + d) – b Ã— (c + d) = (a Ã— c + a Ã— d) – (b Ã— c + b Ã— d)

= ac + ad – bc – bd

Let,

a= 2x2, b= 5y2, c= x2, d= 3y2

Now,

= 2x2 Ã— (x2 + 3y2) â€“ 5y2 Ã— (x2 + 3y2)

= [(2x2 Ã— x2) + (2x2 Ã— 3y2)] – [(5y2 Ã— x2) + (5y2 Ã— 3y2)]

= [2x4 + 6x2y2 â€“ 5y2x2 â€“ 15y4]

= [2x4 + x2y2 â€“ 15y4]

15. (x3 â€“ y3) (x2 + y2)

Solution:-

Suppose (a – b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) Ã— (c + d) = a Ã— (c + d) – b Ã— (c + d) = (a Ã— c + a Ã— d) – (b Ã— c + b Ã— d)

= ac + ad – bc – bd

Let,

a= x3, b= y3, c= x2, d= y2

Now,

= x3 Ã— (x2 + y2) â€“ y3 Ã— (x2 + y2)

= [(x3 Ã— x2) + (x3 Ã— y2)] – [(y3 Ã— x2) + (y3 Ã— y2)]

= [x5 + x3y2 â€“ y3x2 â€“ y5]

## RS Aggarwal Solutions for Class 7 Maths Chapter 6 – Algebraic Expressions

Chapter 6 – Algebraic Expressions contains 4 exercises and the RS Aggarwal Solutions available on this page provide solutions to the questions present in the exercises. Now, let us have a look at some of the concepts discussed in this chapter.

• Constants and Variables